Model components

Hedonic models (HM) disaggregate the price of a product into the value of its component traits to obtain the contributory value of each attribute (Rosen, 1974).

Logs are required by processors because they contain wood traits to produce specific lumber.

In keeping with HM theory, the log is a differentiated product with attributes can be identified and measured and, therefore monetarized.

We assume competitive markets, and the models developed by Ladd and Martin (1976) and Espinosa and Goodwin (1991) are used as a theoretical framework. We also consider a single product firm where specific log attributes, such as small-end diameter, form and internode length, are arguments in the appearance-grade lumber production function G(t).

If the log processor is assumed to maximize profit subject to the production function G(t), the first order conditions of the profit maximization generate Equation (2) which represents a (appearance-grade lumber). Variable z corresponds to the quantity of the input log used in the production of lumber, t_i is the amount of trait i provided by one unit of input z,

z t_i



 is the

marginal yield of trait t_i in the production of lumber from input z, and ti states that the price paid for the input log is equal to the sum of the hedonic prices of the log traits multiplied by the marginal yield of those traits.

Equation (3.2) may be simplified with the assumption that the marginal product of the trait ti

and ⁱ _Ti z t 



 are constant. This simplification implies that each additional unit of input z

contributes the same amount of the t-th trait to the function G(t). Thus, Equation (3.2) can be written as the following single linear hedonic price function:

1

These assumptions have been consistent with many natural commodity traits (Ladd and Martin 1976; Espinosa and Goodwin 1991). Nevertheless, this study is open to estimate nonlinear functional forms according to the model specification tests.

Linking log prices with their attributes by regressions allows obtaining the parameters of Equation (3.2), which is the foundation of hedonic models.

If attributes are not reflected in prices, but they are observable, measurable and directly related to the quality and value of final products, an alternative approach of value could be used in order to estimate the parameters of Equation(3.2). For example, log internode length is a trait intimately related to quality and prices of Shop products. Thus, longer internodes generate longer Shop pieces with higher prices. However, the log market does not explicitly value this characteristic in unpruned log prices.

This study proposes the use of a log recovery value called conversion return (CR), which represents the theoretical maximum willingness to pay for logs in US $/m³ delivered to the sawmill (Davis and Johnson 1987). The suitability of product recovery studies to value wood traits for breeding purposes has been reported by other studies (e.g., Ernst and Fahey 1986;

Aubry et al. 1998). This indicator corresponds to the residual value of the log after processing, and it is estimated as follows:

1 N

i i i

CR p L PC







where p_i is the price of lumber type i, L_i is the volume of lumber type i contained in one cubic meter of logs, and PC is the processing cost of one cubic meter of logs. Prices of lumber corresponding to the ―Industrials, Specialties, and other items‖ section in the Random Lengths Report (Random Lengths 2008), were directly provided by Random Lengths publications.

These corresponded to the monthly prices series 1995-2008, which were expressed in 2008 using the USA CPI (base 1982-1984:100). The average values of these series were used to estimate the CR. Table 3.3 presents prices and shipping costs of products, as well as log processing costs (Jean P. Lasserre, pers. comm., Forestal Mininco-Chile, March 20, 2008).

Table 3.3 Prices and shipping costs for products and processing costs for logs.

Explanatory variables were measured and estimated from logs and trees. The information at the log level includes SED, FORM, internode indices (MIL, BIL, II_60, II₈₀) and branch measures. However, our hypothesis was that branches would have only a minor influence on the quality and value of appearance products, because the knots are removed as part of the production process – i.e. a remanufacturing plant will use chop saws to remove all knots.

Thus the size of knots has a much lower effect than the distribution of knots, which is considered by the internode index. In fact, the requirements for radiata pine appearance lumber relate only to the length of the clear piece (Kretschmann and Hernandez 2006). If there were specific stiffness or strength requirements, the situation would be different because in that case knots derived of branches would cause downgrade in lumber, as it happens with structural lumber (Chauhan 2006a).

At the tree level, the explanatory variables were diameter at breast height (DBH) and internode length indices. Tree form, BI and products volume per tree were obtained by aggregating the logs for each tree, which meant rebuilding forty trees.

The suitability of a linear functional form for the hedonic models was assessed by the Box-Cox transformation (1964). The objective of this transformation is to identify an appropriate exponent lambda (λ) to obtain the best transformation to achieve data normality. The

The resulting functional form will depend on the value of λ. For instance, if λ is equal to one the transformation is linear.

The hedonic model approach allows estimation of elasticities to assess the sensitivity of log value to changes in wood attributes. The changes in log value and attributes were expressed as

percentages of the average log value and average trait. The elasticity of log value () is the change in CR divided by the change in the attribute, multiplied by the level of the attribute divided by the level of CR. In this way, the elasticity depends on the attributes levels considered in its estimation. Elasticity of log value () is estimated as follows:

CR t t

ε CR ⁱ

i

i *



  (3.6)

where t_i is a trait in the hedonic model and CR is the conversion return of the log. If this elasticity is lower than one (inelastic), there will be a less than proportionate change in relative log value for any change in the wood trait. The opposite is true if the elasticity is greater than one (elastic), when the proportionate change in relative log value is greater than the change in the trait. Thus, it is desirable that the log attributes that contribute to log value, such as SED, FORM and internode length, have elasticity values greater than one.